1. Field of the Invention
This invention is related to the high speed topographic surface and tomographic film thickness profile measurements using white light scanning interferometry.
2. Description of Related Art
It is well known in the science and industrial fields that ellipsometry and spectroscopic reflectometry can be used for highly accurate film thickness measurements. Even though ellipsometry and reflectometry have been developed and improved with several techniques such as variable angles, polarizations and tuneable spectral bandwidth, however, they are typically based on a single point measurement which limits the measurement speed and lateral resolution.
White light scanning interferometry (WLI) has been developed to measure the topographic surface height profile of a sample. WLI uses a low temporal coherence source meaning the interference appears when the path lengths of two interferometer arms are the same, as depicted in FIG. 1. Its low temporal coherence solves the ambiguity problem found in phase shifting interferometry (PSI) and makes absolute position measurements possible by a highly accurate scanning motion.
The result of a WLI measurement is a correlogram for each camera pixel. The height information of each pixel can be found by analyzing each correlogram. An important feature of WLI is that the optical spectrum of the source, which relates to the whole system, can be obtained.
This spectrum is found when the correlogram is analyzed in the Fourier domain.
This Fourier transform analysis has been used for the film thickness measurements by investigating the phase and amplitude in the Fourier domain in the prior art. U.S. Pat. No. 6,545,763 to Seung Woo Kim et al describes a method for calculating film thickness and surface profile from Fourier transform of a measured correlogram. This approach makes use of the spectral phase in the Fourier domain which is compared to a theoretical phase generated by preliminary knowledge of a film (i.e. a refractive index) and modelling.
An optimization technique is used to minimize the errors between the measured and theoretical phases and thus the surface height (h) and film thickness (d) are calculated. This approach can measure the film thickness below 1 μm.
However, two disadvantages to this approach are that the two-dimensional optimization process (h, d) is time consuming and setting the scanning range of h and d during the optimization makes real time measurements impossible.
U.S. Pat. No. 7,612,891 to Der-Shen Wan shows another method for measuring films wherein the Fourier amplitude, rather than the phase, is used as a comparison parameter between the measurement and the theoretical model.
The fundamental principle is similar to spectroscopic reflectometry, but the difference is in the methodology of the spectral density functions.
Spectroscopic reflectometry uses a spectrometer to analyze the spectral density function while this patent method measures the spectral density function by the Fourier transform of the correlogram (obtained from WLI). This technique is called Fourier transform spectroscopy. The smooth variation of Fourier amplitude caused by a very thin film can allows more reliable thickness measurements when compared to Fourier phase method.
Other methods using the Fourier amplitude are shown in the U.S. Pat. No. 7,755,768 to Daniel Mansfield. Here, a function (called the helical conjugate function), based on the Fourier amplitude, is defined. The film thickness is calculated by optimizing this function compared to the theoretical value.
However, in both cases, the preliminary experiments with the reflectance standard such as silicon show that these methods are limited due to their slow measurement speed and in its possible applications.
Still another method for measuring the film thickness combines the variable angle micro-ellipsometry principle with WLI as shown in U.S. Pat. No. 7,315,382 and U.S. Pat. No. 7,324,210 to Peter J. De Groot.
This approach uses a high numerical aperture (NA) objective to provide a range of incident angles, which is mathematically resolved by Fourier analysis of the correlogram. The angle-resolved analysis is similar to the Fourier phase method because the optimization with the theoretical model is the same.
But instead of the broadband source, this method uses a narrowband source with high NA objectives to obtain the amplitude and phase according to the incident angles. Thus this method must be applied to the high NA objectives, which have a wide range of incident angles.